Equivalences of Riemann Integral Based on p -Norm

Ray-Ming Chen
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Ray-Ming Chen: School of Mathematics and Statistics, Baise University, No.21 Zhongshan Road, Baise 533000, Guangxi, China

Mathematics, 2018, vol. 6, issue 9, 1-10

Abstract: In the usual Riemann integral setting, the Riemann norm or a mesh is adopted for Riemann sums. In this article, we use the p -norm to define the p -integral and show the equivalences between the Riemann integral and the p -integral. The p -norm provides an alternative approach to define the Riemann integral. Based on this norm, we also derive some other equivalences of the Riemann integral and the p -integral.

Keywords: p -integral; Riemann integral; Darboux integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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